I agree clean it up, refill the diff with gear oil and see if you still have a leak before moving on to replacing anything.
When it comes to presses, the bigger the better, I know that anyone who has ever pressed a new front wheel bearing onto the hubs of these T4Rs has said you need a 20 ton press, so I'm not sure if the 12 ton is good enough for the rear or you need a 20 ton for that as well, either way you may want to check Harbor Freight for a press if you have one close to you...but you may also want to check around to see what a machine shop would charge you to do the pressing if you bring it to them....unless you think you would have other uses for having a press of your own.
On another note when you pull the axle be sure to check it where the seal contacts it for a wear groove, if it has a groove the new seal may not seal properly, I know of a couple of guys who replaced their seal and it still leaked because after many many miles the original seal had worn a groove in the axle, hard to imagine rubber wearing a groove into steel but it can happen after a long enough time.
Edit [MENTION=698138]slonny[/MENTION] , I tried to watch the Youtube video you posted but the link appears to be bad, also you will need more than just the press to get the bearing pressed off and back on the axle, here's a link to a video that shows what else you need other than a press, also some other good info for doing this job.
Rear Axle Bearing Replacement on 4th or 5th gen 4runner Tacoma - How to Press Out Rear Wheel Bearing - YouTube